Solve for $x$ : $ 6|x - 5| + 9 = -4|x - 5| + 5 $
Explanation: Add $ {4|x - 5|} $ to both sides: $ \begin{eqnarray} 6|x - 5| + 9 &=& -4|x - 5| + 5 \\ \\ { + 4|x - 5|} && { + 4|x - 5|} \\ \\ 10|x - 5| + 9 &=& 5 \end{eqnarray} $ Subtract ${9}$ from both sides: $ \begin{eqnarray} 10|x - 5| + 9 &=& 5 \\ \\ { - 9} &=& { - 9} \\ \\ 10|x - 5| &=& -4 \end{eqnarray} $ Divide both sides by ${10}$ $ \dfrac{10|x - 5|} {{10}} = \dfrac{-4} {{10}} $ Simplify: $ |x - 5| = -\dfrac{2}{5}$ The absolute value cannot be negative. Therefore, there is no solution.